Homework 07

Read: Finish Section 2.5, and start Section 2.6.

• There is a lot to read in 2.6—try to go slowly and carefully.

Turn in: 2.63, 2.64, 2.65, 2.68, 2.69, 2.71

• For 2.65, you should be able to create a proof without making a table. Try something like this:

  “Suppose that the element $b$ appears twice in the row corresponding to $g$.” What does this mean? There should be two different columns, which correspond to two different group elements $h_1$ and $h_2$, such that…

Extra practice: 2.66, 2.67(a,b,c)

• For 2.67, remember that earlier we found that the order of $\operatorname{Spin}_{3\times3}$ (i.e. the number of net actions) is equal to the number of scrambled Spinpossible boards (since each net action can be associated to the board that results when the action is applied to the solved board). A similar principle applies to $\operatorname{Spin}_{1\times2}$